Abstract

A photorefractive nonlinear joint-transform correlator based on the incoherent-to-coherent conversion is presented and analyzed. The nonlinearity of this incoherent-erasure joint-transform correlator (IEJTC) is tunable from the classical-matched to the phase-extraction limit. Correlation peak intensity, sharpness, and discrimination ability increase with the incoherent beam intensity. At easily achievable incoherent-to-coherent beam intensity ratios the IEJTC has its optimal performance, at which the IEJTC approaches the performance of the inverse filter for clean inputs and surpasses the inverse filter performance for noisy inputs. We examine this nonlinearity by using the transform method of analysis and computer simulations. Our study focuses on the effect of saturation on the correlation ability. Our results provide an explanation of why extending the severity of saturation by increasing the incoherent-to-coherent intensity ratio beyond a turning point results in lower optical efficiency, degraded correlation peak, and increased higher-order harmonics.

© 1996 Optical Society of America

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References

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  1. J. Khoury, G. Asimellis, C. Woods, “Incoherent-erasure joint-transform correlator,” Opt. Lett. 20, 2321–2323 (1995).
    [CrossRef] [PubMed]
  2. Y. Shi, D. Psaltis, A. Marrakchi, A. R. Tanguay, “Photorefractive incoherent-to-coherent optical converter,” Appl. Opt. 22, 3665–3667 (1983).
    [CrossRef] [PubMed]
  3. J. Khoury, M. Cronin-Golomb, P. Gianino, C. Woods, “Photorefractive two-beam coupling nonlinear joint-transform correlator,” J. Opt. Soc. Am. B 11, 2167–2174 (1994).
    [CrossRef]
  4. J. Khoury, J. Kane, G. Asimellis, M. Cronin-Golomb, C. Woods, “All optical nonlinear joint Fourier transform correlator,” Appl. Opt. 33, 8216–8225 (1994).
    [CrossRef] [PubMed]
  5. G. Asimellis, M. Cronin-Golomb, J. Khoury, J. Kane, C. Woods, “Analysis of the dual discrimination ability of the two-port photorefractive joint transform correlator,” Appl. Opt. 34, 8154–8166 (1995).
    [CrossRef] [PubMed]
  6. G. Asimellis, J. Khoury, J. Kane, C. Woods, “Two-port photorefractive joint-transform correlator,” Opt. Lett. 20, 2517–2519 (1995).
    [CrossRef] [PubMed]
  7. D. O. North, “An analysis of the factors which determine signal/noise discriminations in pulsed carrier systems,” Proc. IEEE 51, 1016–1027 (1963).
    [CrossRef]
  8. K. H. Fielding, J. L. Horner, “Clutter effects in optical correlators,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. SPIE1151, 130–137 (1990).
    [CrossRef]
  9. A. Tanone, C. M. Uang, F. T. S. Yu, E. C. Tam, D. A. Gregory, “Effects of thresholding in joint-transform correlation,” Appl. Opt. 31, 4816–4822 (1992).
    [CrossRef] [PubMed]
  10. H. Rajbenbach, “Dynamic holography in optical pattern recognition,” in Optical Pattern Recognition V, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE2237, 329–346 (1994).
    [CrossRef]
  11. J. L. Horner, USAF Rome Laboratories, Optical Signal Processing Branch (personal communication, 1995).
  12. C. S. Weaver, J. W. Goodman, “Technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
    [CrossRef] [PubMed]
  13. J. E. Rau, “Detection of difference in real distributions,”J. Opt. Soc. Am. 56, 1490–1494 (1966).
    [CrossRef]
  14. D. A. Gregory, “Real-time pattern recognition using a modified LCTV in a coherent optical correlator,” Appl. Opt. 25, 467–468 (1986).
    [CrossRef] [PubMed]
  15. B. Javidi, J. L. Horner, “Single SLM joint transform correlator,” Opt. Eng. 28, 1027–1032 (1989).
  16. B. Javidi, J. Wang, “Design of filters to detect a noisy target in nonoverlapping background noise,” J. Opt. Soc. Am. A 11, 2604–2612 (1994).
    [CrossRef]
  17. B. Javidi, J. Wang, “Optimum filter for detection of a target in nonoverlapping scene noise,” Appl. Opt. 33, 4454–4458 (1994).
    [CrossRef] [PubMed]
  18. B. Javidi, “Nonlinear joint power spectrum based optical correlation,” Appl. Opt. 28, 2358–2367 (1989).
    [CrossRef] [PubMed]
  19. T. J. Grycewicz, “Applying time modulation to the joint transform correlator,” Opt. Eng. 33, 1813–1820 (1994).
    [CrossRef]
  20. M. S. Alam, M. A. Karim, “Joint-transform correlation under varying illumination,” Appl. Opt. 32, 4351–4356 (1993).
    [CrossRef] [PubMed]
  21. F. Cheng, P. Andres, F. T. S. Yu, D. A. Gregory, “Intensity compensation fiber for joint transform correlation peak enhancement,” Appl. Opt. 32, 4357–4364 (1993).
    [CrossRef] [PubMed]
  22. H. Rajbenbach, S. Bann, J. P. Huignard, “A compact photorefractive joint transform correlator for industrial recognition tasks,” in Optical Computing, Vol. 6 of 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 260–263.
  23. J. O. White, A. Yariv, “Real-time image processing via four-wave mixing,” Appl. Phys. Lett. 37, 5–7 (1980).
    [CrossRef]
  24. M. R. Weiss, A. Siahmakoun, “Autocorrelation via two-wave mixing in barium titanate,” Opt. Eng. 30, 403–406 (1991).
    [CrossRef]
  25. D. A. Jared, K. M. Johnson, G. Moddel, “Joint transform correlator using amorphous silicon ferroelectric liquid crystal spatial modulator,” Opt. Commun. 76, 97–102 (1990).
    [CrossRef]
  26. T. D. Hudson, D. A. Gregory, “JTC using an optically addressed FLC SLM,” Appl. Opt. 29, 1064–1066 (1990).
    [CrossRef] [PubMed]
  27. L. Guibert, G. Keryer, A. Servel, M. Attia, H. MacKenzie, P. Pellat-Finet, J. L. de Bougrenet de la Tocnaye, “Onboard optical joint transform correlator for real-time road sign recognition,” Opt. Eng. 34, 135–143 (1995).
    [CrossRef]
  28. M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12–29 (1984).
    [CrossRef]
  29. F. T. S. Yu, Y. S. Cheng, “White-light joint-transform correlator,” Opt. Lett. 15, 192–194 (1989).
    [CrossRef]
  30. M. Cronin-Golomb, “Achromatic volume holography using dispersive compensation for grating tilt,” Appl. Opt. 14, 1297–1299 (1989).
  31. M. W. McCall, C. R. Petts, “Grating modification in degenerate four wave mixing,” Opt. Commun. 53, 7–12 (1985).
    [CrossRef]
  32. N. A. Vianos, R. W. Eason, “Real time enhancement by active spatial filtering via five wave mixing in photorefractive BSO,” Opt. Commun. 59, 167–172 (1986).
    [CrossRef]
  33. A. Marrakchi, A. R. Tanguay, J. Yu, D. Psaltis, “Physical characterization of the photorefractive incoherent-to-coherent optical converter,” Opt. Eng. 24, 124–131 (1985).
    [CrossRef]
  34. H. Bartlet, J. L. Horner, “Improving binary phase correlation filters using iterative techniques,” Appl. Opt. 24, 2894–2897 (1985).
    [CrossRef]
  35. J. L. Horner, “Metrics for assessing pattern-recognition performance,” Appl. Opt. 31, 165–166 (1992).
    [CrossRef] [PubMed]
  36. W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signal and Noise (McGraw-Hill, New York, 1958).
  37. W. Magnus, F. Oberhettinger, Formulas and Theorems for the Special Functions of Mathematical Physics (Chelsea, New York, 1966), Vol. I, Chap. 3, Article 1.

1995

1994

1993

1992

1991

M. R. Weiss, A. Siahmakoun, “Autocorrelation via two-wave mixing in barium titanate,” Opt. Eng. 30, 403–406 (1991).
[CrossRef]

1990

D. A. Jared, K. M. Johnson, G. Moddel, “Joint transform correlator using amorphous silicon ferroelectric liquid crystal spatial modulator,” Opt. Commun. 76, 97–102 (1990).
[CrossRef]

T. D. Hudson, D. A. Gregory, “JTC using an optically addressed FLC SLM,” Appl. Opt. 29, 1064–1066 (1990).
[CrossRef] [PubMed]

1989

1986

D. A. Gregory, “Real-time pattern recognition using a modified LCTV in a coherent optical correlator,” Appl. Opt. 25, 467–468 (1986).
[CrossRef] [PubMed]

N. A. Vianos, R. W. Eason, “Real time enhancement by active spatial filtering via five wave mixing in photorefractive BSO,” Opt. Commun. 59, 167–172 (1986).
[CrossRef]

1985

A. Marrakchi, A. R. Tanguay, J. Yu, D. Psaltis, “Physical characterization of the photorefractive incoherent-to-coherent optical converter,” Opt. Eng. 24, 124–131 (1985).
[CrossRef]

H. Bartlet, J. L. Horner, “Improving binary phase correlation filters using iterative techniques,” Appl. Opt. 24, 2894–2897 (1985).
[CrossRef]

M. W. McCall, C. R. Petts, “Grating modification in degenerate four wave mixing,” Opt. Commun. 53, 7–12 (1985).
[CrossRef]

1984

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12–29 (1984).
[CrossRef]

1983

1980

J. O. White, A. Yariv, “Real-time image processing via four-wave mixing,” Appl. Phys. Lett. 37, 5–7 (1980).
[CrossRef]

1966

1963

D. O. North, “An analysis of the factors which determine signal/noise discriminations in pulsed carrier systems,” Proc. IEEE 51, 1016–1027 (1963).
[CrossRef]

Alam, M. S.

Andres, P.

Asimellis, G.

Attia, M.

L. Guibert, G. Keryer, A. Servel, M. Attia, H. MacKenzie, P. Pellat-Finet, J. L. de Bougrenet de la Tocnaye, “Onboard optical joint transform correlator for real-time road sign recognition,” Opt. Eng. 34, 135–143 (1995).
[CrossRef]

Bann, S.

H. Rajbenbach, S. Bann, J. P. Huignard, “A compact photorefractive joint transform correlator for industrial recognition tasks,” in Optical Computing, Vol. 6 of 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 260–263.

Bartlet, H.

Cheng, F.

Cheng, Y. S.

Cronin-Golomb, M.

Davenport, W. B.

W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signal and Noise (McGraw-Hill, New York, 1958).

de Bougrenet de la Tocnaye, J. L.

L. Guibert, G. Keryer, A. Servel, M. Attia, H. MacKenzie, P. Pellat-Finet, J. L. de Bougrenet de la Tocnaye, “Onboard optical joint transform correlator for real-time road sign recognition,” Opt. Eng. 34, 135–143 (1995).
[CrossRef]

Eason, R. W.

N. A. Vianos, R. W. Eason, “Real time enhancement by active spatial filtering via five wave mixing in photorefractive BSO,” Opt. Commun. 59, 167–172 (1986).
[CrossRef]

Fielding, K. H.

K. H. Fielding, J. L. Horner, “Clutter effects in optical correlators,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. SPIE1151, 130–137 (1990).
[CrossRef]

Fischer, B.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12–29 (1984).
[CrossRef]

Gianino, P.

Goodman, J. W.

Gregory, D. A.

Grycewicz, T. J.

T. J. Grycewicz, “Applying time modulation to the joint transform correlator,” Opt. Eng. 33, 1813–1820 (1994).
[CrossRef]

Guibert, L.

L. Guibert, G. Keryer, A. Servel, M. Attia, H. MacKenzie, P. Pellat-Finet, J. L. de Bougrenet de la Tocnaye, “Onboard optical joint transform correlator for real-time road sign recognition,” Opt. Eng. 34, 135–143 (1995).
[CrossRef]

Horner, J. L.

J. L. Horner, “Metrics for assessing pattern-recognition performance,” Appl. Opt. 31, 165–166 (1992).
[CrossRef] [PubMed]

B. Javidi, J. L. Horner, “Single SLM joint transform correlator,” Opt. Eng. 28, 1027–1032 (1989).

H. Bartlet, J. L. Horner, “Improving binary phase correlation filters using iterative techniques,” Appl. Opt. 24, 2894–2897 (1985).
[CrossRef]

J. L. Horner, USAF Rome Laboratories, Optical Signal Processing Branch (personal communication, 1995).

K. H. Fielding, J. L. Horner, “Clutter effects in optical correlators,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. SPIE1151, 130–137 (1990).
[CrossRef]

Hudson, T. D.

Huignard, J. P.

H. Rajbenbach, S. Bann, J. P. Huignard, “A compact photorefractive joint transform correlator for industrial recognition tasks,” in Optical Computing, Vol. 6 of 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 260–263.

Jared, D. A.

D. A. Jared, K. M. Johnson, G. Moddel, “Joint transform correlator using amorphous silicon ferroelectric liquid crystal spatial modulator,” Opt. Commun. 76, 97–102 (1990).
[CrossRef]

Javidi, B.

Johnson, K. M.

D. A. Jared, K. M. Johnson, G. Moddel, “Joint transform correlator using amorphous silicon ferroelectric liquid crystal spatial modulator,” Opt. Commun. 76, 97–102 (1990).
[CrossRef]

Kane, J.

Karim, M. A.

Keryer, G.

L. Guibert, G. Keryer, A. Servel, M. Attia, H. MacKenzie, P. Pellat-Finet, J. L. de Bougrenet de la Tocnaye, “Onboard optical joint transform correlator for real-time road sign recognition,” Opt. Eng. 34, 135–143 (1995).
[CrossRef]

Khoury, J.

MacKenzie, H.

L. Guibert, G. Keryer, A. Servel, M. Attia, H. MacKenzie, P. Pellat-Finet, J. L. de Bougrenet de la Tocnaye, “Onboard optical joint transform correlator for real-time road sign recognition,” Opt. Eng. 34, 135–143 (1995).
[CrossRef]

Magnus, W.

W. Magnus, F. Oberhettinger, Formulas and Theorems for the Special Functions of Mathematical Physics (Chelsea, New York, 1966), Vol. I, Chap. 3, Article 1.

Marrakchi, A.

A. Marrakchi, A. R. Tanguay, J. Yu, D. Psaltis, “Physical characterization of the photorefractive incoherent-to-coherent optical converter,” Opt. Eng. 24, 124–131 (1985).
[CrossRef]

Y. Shi, D. Psaltis, A. Marrakchi, A. R. Tanguay, “Photorefractive incoherent-to-coherent optical converter,” Appl. Opt. 22, 3665–3667 (1983).
[CrossRef] [PubMed]

McCall, M. W.

M. W. McCall, C. R. Petts, “Grating modification in degenerate four wave mixing,” Opt. Commun. 53, 7–12 (1985).
[CrossRef]

Moddel, G.

D. A. Jared, K. M. Johnson, G. Moddel, “Joint transform correlator using amorphous silicon ferroelectric liquid crystal spatial modulator,” Opt. Commun. 76, 97–102 (1990).
[CrossRef]

North, D. O.

D. O. North, “An analysis of the factors which determine signal/noise discriminations in pulsed carrier systems,” Proc. IEEE 51, 1016–1027 (1963).
[CrossRef]

Oberhettinger, F.

W. Magnus, F. Oberhettinger, Formulas and Theorems for the Special Functions of Mathematical Physics (Chelsea, New York, 1966), Vol. I, Chap. 3, Article 1.

Pellat-Finet, P.

L. Guibert, G. Keryer, A. Servel, M. Attia, H. MacKenzie, P. Pellat-Finet, J. L. de Bougrenet de la Tocnaye, “Onboard optical joint transform correlator for real-time road sign recognition,” Opt. Eng. 34, 135–143 (1995).
[CrossRef]

Petts, C. R.

M. W. McCall, C. R. Petts, “Grating modification in degenerate four wave mixing,” Opt. Commun. 53, 7–12 (1985).
[CrossRef]

Psaltis, D.

A. Marrakchi, A. R. Tanguay, J. Yu, D. Psaltis, “Physical characterization of the photorefractive incoherent-to-coherent optical converter,” Opt. Eng. 24, 124–131 (1985).
[CrossRef]

Y. Shi, D. Psaltis, A. Marrakchi, A. R. Tanguay, “Photorefractive incoherent-to-coherent optical converter,” Appl. Opt. 22, 3665–3667 (1983).
[CrossRef] [PubMed]

Rajbenbach, H.

H. Rajbenbach, “Dynamic holography in optical pattern recognition,” in Optical Pattern Recognition V, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE2237, 329–346 (1994).
[CrossRef]

H. Rajbenbach, S. Bann, J. P. Huignard, “A compact photorefractive joint transform correlator for industrial recognition tasks,” in Optical Computing, Vol. 6 of 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 260–263.

Rau, J. E.

Root, W. L.

W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signal and Noise (McGraw-Hill, New York, 1958).

Servel, A.

L. Guibert, G. Keryer, A. Servel, M. Attia, H. MacKenzie, P. Pellat-Finet, J. L. de Bougrenet de la Tocnaye, “Onboard optical joint transform correlator for real-time road sign recognition,” Opt. Eng. 34, 135–143 (1995).
[CrossRef]

Shi, Y.

Siahmakoun, A.

M. R. Weiss, A. Siahmakoun, “Autocorrelation via two-wave mixing in barium titanate,” Opt. Eng. 30, 403–406 (1991).
[CrossRef]

Tam, E. C.

Tanguay, A. R.

A. Marrakchi, A. R. Tanguay, J. Yu, D. Psaltis, “Physical characterization of the photorefractive incoherent-to-coherent optical converter,” Opt. Eng. 24, 124–131 (1985).
[CrossRef]

Y. Shi, D. Psaltis, A. Marrakchi, A. R. Tanguay, “Photorefractive incoherent-to-coherent optical converter,” Appl. Opt. 22, 3665–3667 (1983).
[CrossRef] [PubMed]

Tanone, A.

Uang, C. M.

Vianos, N. A.

N. A. Vianos, R. W. Eason, “Real time enhancement by active spatial filtering via five wave mixing in photorefractive BSO,” Opt. Commun. 59, 167–172 (1986).
[CrossRef]

Wang, J.

Weaver, C. S.

Weiss, M. R.

M. R. Weiss, A. Siahmakoun, “Autocorrelation via two-wave mixing in barium titanate,” Opt. Eng. 30, 403–406 (1991).
[CrossRef]

White, J. O.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12–29 (1984).
[CrossRef]

J. O. White, A. Yariv, “Real-time image processing via four-wave mixing,” Appl. Phys. Lett. 37, 5–7 (1980).
[CrossRef]

Woods, C.

Yariv, A.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12–29 (1984).
[CrossRef]

J. O. White, A. Yariv, “Real-time image processing via four-wave mixing,” Appl. Phys. Lett. 37, 5–7 (1980).
[CrossRef]

Yu, F. T. S.

Yu, J.

A. Marrakchi, A. R. Tanguay, J. Yu, D. Psaltis, “Physical characterization of the photorefractive incoherent-to-coherent optical converter,” Opt. Eng. 24, 124–131 (1985).
[CrossRef]

Appl. Opt.

J. Khoury, J. Kane, G. Asimellis, M. Cronin-Golomb, C. Woods, “All optical nonlinear joint Fourier transform correlator,” Appl. Opt. 33, 8216–8225 (1994).
[CrossRef] [PubMed]

G. Asimellis, M. Cronin-Golomb, J. Khoury, J. Kane, C. Woods, “Analysis of the dual discrimination ability of the two-port photorefractive joint transform correlator,” Appl. Opt. 34, 8154–8166 (1995).
[CrossRef] [PubMed]

Y. Shi, D. Psaltis, A. Marrakchi, A. R. Tanguay, “Photorefractive incoherent-to-coherent optical converter,” Appl. Opt. 22, 3665–3667 (1983).
[CrossRef] [PubMed]

A. Tanone, C. M. Uang, F. T. S. Yu, E. C. Tam, D. A. Gregory, “Effects of thresholding in joint-transform correlation,” Appl. Opt. 31, 4816–4822 (1992).
[CrossRef] [PubMed]

C. S. Weaver, J. W. Goodman, “Technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
[CrossRef] [PubMed]

D. A. Gregory, “Real-time pattern recognition using a modified LCTV in a coherent optical correlator,” Appl. Opt. 25, 467–468 (1986).
[CrossRef] [PubMed]

B. Javidi, J. Wang, “Optimum filter for detection of a target in nonoverlapping scene noise,” Appl. Opt. 33, 4454–4458 (1994).
[CrossRef] [PubMed]

B. Javidi, “Nonlinear joint power spectrum based optical correlation,” Appl. Opt. 28, 2358–2367 (1989).
[CrossRef] [PubMed]

M. S. Alam, M. A. Karim, “Joint-transform correlation under varying illumination,” Appl. Opt. 32, 4351–4356 (1993).
[CrossRef] [PubMed]

F. Cheng, P. Andres, F. T. S. Yu, D. A. Gregory, “Intensity compensation fiber for joint transform correlation peak enhancement,” Appl. Opt. 32, 4357–4364 (1993).
[CrossRef] [PubMed]

T. D. Hudson, D. A. Gregory, “JTC using an optically addressed FLC SLM,” Appl. Opt. 29, 1064–1066 (1990).
[CrossRef] [PubMed]

M. Cronin-Golomb, “Achromatic volume holography using dispersive compensation for grating tilt,” Appl. Opt. 14, 1297–1299 (1989).

H. Bartlet, J. L. Horner, “Improving binary phase correlation filters using iterative techniques,” Appl. Opt. 24, 2894–2897 (1985).
[CrossRef]

J. L. Horner, “Metrics for assessing pattern-recognition performance,” Appl. Opt. 31, 165–166 (1992).
[CrossRef] [PubMed]

Appl. Phys. Lett.

J. O. White, A. Yariv, “Real-time image processing via four-wave mixing,” Appl. Phys. Lett. 37, 5–7 (1980).
[CrossRef]

IEEE J. Quantum Electron.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12–29 (1984).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Commun.

M. W. McCall, C. R. Petts, “Grating modification in degenerate four wave mixing,” Opt. Commun. 53, 7–12 (1985).
[CrossRef]

N. A. Vianos, R. W. Eason, “Real time enhancement by active spatial filtering via five wave mixing in photorefractive BSO,” Opt. Commun. 59, 167–172 (1986).
[CrossRef]

D. A. Jared, K. M. Johnson, G. Moddel, “Joint transform correlator using amorphous silicon ferroelectric liquid crystal spatial modulator,” Opt. Commun. 76, 97–102 (1990).
[CrossRef]

Opt. Eng.

A. Marrakchi, A. R. Tanguay, J. Yu, D. Psaltis, “Physical characterization of the photorefractive incoherent-to-coherent optical converter,” Opt. Eng. 24, 124–131 (1985).
[CrossRef]

L. Guibert, G. Keryer, A. Servel, M. Attia, H. MacKenzie, P. Pellat-Finet, J. L. de Bougrenet de la Tocnaye, “Onboard optical joint transform correlator for real-time road sign recognition,” Opt. Eng. 34, 135–143 (1995).
[CrossRef]

M. R. Weiss, A. Siahmakoun, “Autocorrelation via two-wave mixing in barium titanate,” Opt. Eng. 30, 403–406 (1991).
[CrossRef]

T. J. Grycewicz, “Applying time modulation to the joint transform correlator,” Opt. Eng. 33, 1813–1820 (1994).
[CrossRef]

B. Javidi, J. L. Horner, “Single SLM joint transform correlator,” Opt. Eng. 28, 1027–1032 (1989).

Opt. Lett.

Proc. IEEE

D. O. North, “An analysis of the factors which determine signal/noise discriminations in pulsed carrier systems,” Proc. IEEE 51, 1016–1027 (1963).
[CrossRef]

Other

K. H. Fielding, J. L. Horner, “Clutter effects in optical correlators,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. SPIE1151, 130–137 (1990).
[CrossRef]

H. Rajbenbach, “Dynamic holography in optical pattern recognition,” in Optical Pattern Recognition V, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE2237, 329–346 (1994).
[CrossRef]

J. L. Horner, USAF Rome Laboratories, Optical Signal Processing Branch (personal communication, 1995).

H. Rajbenbach, S. Bann, J. P. Huignard, “A compact photorefractive joint transform correlator for industrial recognition tasks,” in Optical Computing, Vol. 6 of 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 260–263.

W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signal and Noise (McGraw-Hill, New York, 1958).

W. Magnus, F. Oberhettinger, Formulas and Theorems for the Special Functions of Mathematical Physics (Chelsea, New York, 1966), Vol. I, Chap. 3, Article 1.

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Figures (12)

Fig. 1
Fig. 1

Proposed experimental arrangement. BS, beam splitter.

Fig. 2
Fig. 2

IEJTC input–output curve: normalized phase-conjugate beam amplitude versus relative spectral energy. Dotted–dashed curve, linear response limit; dashed line, inverse response limit.

Fig. 3
Fig. 3

Computer simulations with the similar disks: (a) Reference (top) and scene (bottom) images. Correlation peak intensity plots for the two disks using (a): (b) matched filter, (c) phase-only filter, (d) inverse filter.

Fig. 4
Fig. 4

Computer simulations with the tanks: (a) Reference (top) and scene (bottom) images. Correlation peak intensity plots for the two disks using (a): (b) matched filter, (c) phase-only filter, (d) inverse filter.

Fig. 5
Fig. 5

Computer simulations of the IEJTC with the disks shown in Fig. 3(a) at increasing beam ratio: plots of the intensity array around the correlation peak with beam ratios (a) 10−2, (b) 101, (c) 104, and (d) 107.

Fig. 6
Fig. 6

Computer simulations of the IEJTC with the tanks shown in Fig. 4(a) at increasing beam ratio: plots of the intensity array around the correlation peak with beam ratios (a) 10−2, (b) 101, (c) 104, and (d) 107.

Fig. 7
Fig. 7

Input planes used for discrimination ability measurements: (a) a tank versus the same tank, (b) a tank versus an armored vehicle (M113). The center-to-center separation was 128 pixels.

Fig. 8
Fig. 8

Comparative plots of the correlation peak amplitudes for intermediate, large, and very large beam ratios. The left-hand column corresponds to the tank versus tank, and the right-hand column corresponds to the tank versus the armored vehicle.

Fig. 9
Fig. 9

Optical efficiency envelope and correlation coefficients for the first three orders versus beam ratio.

Fig. 10
Fig. 10

Overall weighting functions for the first three orders (k = 1, 2, and 3) versus beam ratio.

Fig. 11
Fig. 11

Plots of the entire correlation plane (amplitude array) with the clean disks: (a) small beam ratio meff = 10−2, (b) intermediate beam ratio meff = 101, (c) large beam ratio meff = 104, (d) very large beam ratio meff = 107. The dc shown is clipped; the maximum values of the clipped dc spots are (a) 511, (b) 505, (c) 259, and (d) 72.

Fig. 12
Fig. 12

Plots of the entire correlation plane (amplitude array) with the tank in desert noise: (a) small beam ratio meff = 10−2, (b) intermediate beam ratio meff = 101, (c) large beam ratio meff = 104, (d) very large beam ratio meff = 107. The dc shown is clipped; the maximum values of the clipped dc spots are (a) 511, (b) 505, (c) 259, and (d) 0.99.

Tables (2)

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Table 1 PNR, SNR, and Peak Intensity Measurements for the Disk Inputs with the IEJTC at Various Operating Points, the Matched Filter, the Phase-Only Filter, and the Inverse Filter

Tables Icon

Table 2 PNR, SNR, and Peak Intensity Measurements for the Tank Inputs with the IEJTC at Various Operating Points, the Matched Filter, the Phase-Only Filter, and the Inverse Filter

Equations (38)

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G ( ν x , ν y ) = R ( ν x , ν y ) exp [ i ϕ R ( ν x , ν y ) + i y 0 ν y ] + S ( ν x , ν y ) exp [ i ϕ S ( ν x , ν y ) - i y 0 ν y ] .
f CL ( ν x , ν y ) = S 2 ( ν x , ν y ) + R 2 ( ν x , ν y ) + S ( ν x , ν y ) R ( ν x , ν y ) exp [ i ϕ S ( ν x , ν y ) - i ϕ R ( ν x , ν y ) ] exp ( - i 2 y 0 ν y ) + c . c . ,
f CL ( ν x , ν y ) R = S = 2 R 2 ( ν x , ν y ) + 2 R 2 ( ν x , ν y ) cos ( 2 ν x , y 0 ) .
μ = 2 A 1 A 4 * A 1 2 + A 2 2 + A 4 2 = 2 A 1 A 4 * I c ,
A 30 = μ A 2 2 γ L = ( A 1 A 4 * ) A 2 I c γ L .
μ eff = μ 1 + I i I c α i λ i α c λ c exp [ ( α c - α i ) L ] R ( ν x , ν y ) + S ( ν x , ν y ) 2 ( λ i f 1 ) 2 ,
A 3 ( ν x , ν y ) = ( A 1 A 4 * ) A 2 γ L I c + I i α i λ i α c λ c exp [ ( α c - α i ) L ] R ( ν x , ν y ) + S ( ν x , ν y ) 2 ( λ i f 1 ) 2 .
f ( ν x , ν y ) = 1 1 + m eff E ( ν x , ν y ) ,
E ( ν x , ν y ) = R ( ν x , ν y ) + S ( ν x , ν y ) 2 E 0 2 ,
m eff = α i λ i α c λ c exp [ ( α c - α i ) L ] E 0 2 ( λ i f 1 ) 2 I i I c ,
A 3 ( ν x , ν y ) = A 30 [ 1 - m eff E ( ν x , ν y ) ] .
A 3 ( ν x , ν y ) = A 30 m eff E ( ν x , ν y ) .
SNR = k max ( 1 n T i = 1 n T k i 2 ) 1 / 2 ,             k i 2 < 0.5 k max ,
PNR = k max ( 1 n - 1 i = 1 n - 1 k i 2 ) 1 / 2 ,             k i = k max ,
f ( ν x , ν y ) R = S = 1 1 + 4 m eff R 2 × k = 0 ( - 2 m eff R 2 1 + 2 m eff R 2 + 1 + 4 m eff R 2 ) k × cos ( 2 k y 0 ν y ) .
f ( ν x , ν y ) R = S = η k = 0 c k cos ( 2 k y 0 ν y ) ,
η = 1 1 + 4 m eff R 2 ,
c k = ( - 2 m eff R 2 1 + 2 m eff R 2 + 1 + 4 m eff R 2 ) k .
f ( ν x , ν y ) R = S = ( 1 - 2 m eff R 2 ) k = 0 ( - 2 m eff R 2 ) k cos ( 2 k y 0 ν y ) .
f ( ν x , ν y ) R = S = 1 4 m eff R 2 k = 0 ( 2 m eff R 2 ) 0 cos ( 2 k y 0 ν y ) .
F ( ω ) = - f ( E ) exp ( - i ω E ) d E ,
f ( E ) = 1 2 π - F ( ω ) exp ( + i ω E ) d ω .
E = S ( ν x , ν y ) + R ( ν x , ν y ) 2 = S 2 ( ν x , ν y ) + S ( ν x , ν y ) × R ( ν x , ν y ) exp [ i ϕ S ( ν x , ν y ) - i ϕ R ( ν x , ν y ) ] × exp ( - i 2 y 0 ν y ) + S ( ν x , ν y ) R ( ν x , ν y ) × exp [ - i ϕ S ( ν x , ν y ) + i ϕ R ( ν x , ν y ) ] exp ( + i 2 y 0 ν y ) + R 2 ( ν x , ν y ) .
f ( E ) = 1 2 π - F ( ω ) exp [ i ω ( R 2 + S 2 ) ] × exp [ i 2 ω R S cos ( 2 y 0 ν y + ϕ R - ϕ S ) ] d ω .
exp [ i m cos ( ω x ) ] = k = - i k J k ( m ) cos [ k ( ω x ) ] ,
f ( E ) = k = 0 H k ( ν x , ν y ) cos [ 2 k y 0 ν y + k ( ϕ R - ϕ s ) ] ,
H k ( ν x , ν y ) = ɛ k 2 π i k - F ( ω ) exp [ i ω ( r 2 + S 2 ) ] × J k ( 2 ω R S ) d ω
f ( E ) = 1 1 + m eff E ,
F ( ω ) = - i sgn ( ω ) π m eff exp ( i ω m eff ) ,
H k ( ν x , ν y ) = - i k + 1 ɛ k 2 0 exp { i r [ 1 + m eff ( R 2 + S 2 ) ] } × J k ( 2 r m eff R S ) d r ,
0 exp ( i b z ) J k ( a z ) d z = i k + 1 a k b 2 - a 2 ( b + b 2 - a 2 ) k ,
H 0 ( ν x , ν y ) = 1 { [ 1 + m eff ( R - S ) 2 ] [ 1 + m eff ( R + S ) 2 ] } 1 / 2 ,
H 1 ( ν x , ν y ) = 1 { [ 1 + m e f f ( R - S ) 2 ] [ 1 + m e f f ( R + S ) 2 ] } 1 / 2 ( 2 m eff R S 1 + m eff ( R 2 + S 2 ) + { [ 1 + m eff ( R - S ) 2 ] [ 1 + m eff ( R + S ) 2 ] } 1 / 2 ) ,
H 2 ( ν x , ν y ) = 1 { [ 1 + m eff ( R - S ) 2 ] [ 1 + m eff ( R + S ) 2 ] } 1 / 2 ( 2 m eff R S 1 + m eff ( R 2 + S 2 ) + { [ 1 + m eff ( R - S ) 2 ] [ 1 + m eff ( R + S ) 2 ] } 1 / 2 ) .
f ( ν x , ν y ) R = S = k = 0 H k ( ν x , ν y ) R = S cos ( 2 k y 0 ν y ) ,
H k ( ν x , ν y ) R = S = - i k + 1 ɛ k 2 0 exp [ i r ( 1 + 2 m eff R 2 ) ] × J k ( 2 r m eff R 2 ) d r
H k ( ν x , ν y ) R = S = 1 1 + 4 m eff R 2 × ( - 2 m eff R 2 1 + 2 m eff R 2 + 1 + 4 m eff R 2 ) k .
f ( ν x , ν y ) R = S = 1 1 + 4 m eff R 2 × k = 0 ( - 2 m eff R 2 1 + 2 m eff R 2 + 1 + 4 m eff R 2 ) k × cos ( 2 k y 0 ν y ) .

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